Nichrome wire heater optimisation

Hi, I am designing a plastic recycler and I need advice on choosing gauge of some nichrome wire. I want the heater to reach around 220 degrees C and I will be powering it with a laptop charger (19v 7.1 amps). Temperature control will be achieved with a PID controller.

The nichrome wire will be wrapped around a 21mm outer diameter tube and 17mm inner diameter (I'm thinking copper). The heater has to be able to melt the plastic before it reaches a 3mm hole at the end of the tube.

I used Q=mCdT to find the energy needed to melt the plastic pellets as they travel down the tube at a given velocity, where Q is the energy required, m is the mass flow, and dT is the change in temperature required. To raise the plastic by 200 degrees it will need 628J/s

Using power equations I estimated the power dissipated by a coil given the length of the tube (0.1m), gauge of the wire, and voltage input. The power dissipated by my coil ends up being 120watts.

My question is, do the values for energy_needed and power_dissipation I calculated above seem realistic bearing in mind this will be be a small unit? (the tube is only 10cm long and I'm winding a coil around it once). To me they seem quite high somehow, but then again I'm not sure :/!

Also I want to optimise the design of the coil.
Is it simply a matter varying the gauge of the wire until the power_dissipation = Q or am I overlooking something?